Least‐squares mixed Galerkin formulation for variable‐coefficient fractional differential equations with D‐N boundary condition

Abstract

We propose a least‐squares mixed variational formulation for variable‐coefficient fractional differential equations (FDEs) subject to general Dirichlet‐Neumann boundary condition by splitting the FDE as a system of variable‐coefficient integer‐order equation and constant‐coefficient FDE. The main contributions of this article are to establish a new regularity theory of the solution expressed in terms of the smoothness of the right‐hand side only and to develop a decoupled and optimally convergent finite element procedure for the unknown and intermediate variables. Numerical analysis and experiments are conducted to verify these findings.